The second snippet shouldn't be any slower. In both snippets, the regexp is compiled once.

However,

my @regexps = (
   'pattern1',
   'pattern2',
);

for my $s (@strings) {
   for $re (@regexps) {
      something($s =~ /$re/);
   }
}
[download]

is slower than

my @regexps = (
   qr/pattern1/,
   qr/pattern2/,
);

for my $s (@strings) {
   for $re (@regexps) {
      something($s =~ /$re/);
   }
}
[download]

since the former compiles each regexp for each string, while the latter compiles each regexp once.